Within this Program Project, this proposal describes a research plan that seeks to develop computational technology that will give improved estimates of the relative particle alignments and thereby improve the quality of 3-D reconstructions that are produced by a given number of particle images. Currently structural analysis is limited to approximately 10 Angstroms resolution. Our goal is to advance the existing capabilities to extract near atomic resolution 3D structures from the inherently noisy images of single particles by designing new massively parallel algorithms for determination and refinement of orientation parameters. We show in preliminary results that attainment of an optimal 3D structure cannot be guaranteed when current refinement methods are used. Moreover, we demonstrate that when the reference structure used for refinement is systematically distorted the existing refinement procedure can be trapped in a local minimum.Within the framework of this proposal, we will develop computational methods that explore the space of all possible Solutions (of all orientation parameters) from a given set of single particle images. To achieve this goal, we will determine the limitations of currently used algorithms with particular attention to the determination and refinement of the orientation parameters and the generation of the optimal 3D structure given the best estimate of the orientation parameters. The new refinement and optimization algorithms will be formulated in terms of combinatorial optimization. Specifically, the ab initio structure determination will be achieved with heuristic-augmented parallel genetic algorithm. The candidate solutions will be improved using a local search method in which the 3D density map and the orientation parameters are corrected simultaneously. The results will be evaluated with the help of new statistical test that will :measure the quality of 3D reconstruction with respect to the quality of images.The software will be developed in ways that assure full portability and it will be ported within the SPARX and SPIDER systems.